Related papers: Development of the Poincare cross-section method: …
Study of continuous dynamical system through Poincare map is one of the most popular topics in nonlinear analysis. This is done by taking intersections of the orbit of flow by a hyper-plane parallel to one of the coordinate hyper-planes of…
The paper introduces a one dimensional analogy of Poincare's "section" method. Its application to numerical study of sequences of fractional parts is considered. As a result, the possibility of Cantorian structure of time flow is deduced. A…
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a…
Poincar\'e maps and suspension flows are examples of fundamental constructions in the study of dynamical systems. This study aimed to show that these constructions define an adjoint pair of functors if categories of dynamical systems are…
This paper presents a convenient graphical tool for encoding visual patterns (such as image patches and image atoms) as point constellations in a space spanned by perceptual features and with a clear geometrical interpretation. General…
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases…
Scalar features in time-dependent fluid flow are traditionally visualized using 3D representation, and their topology changes over time are often conveyed with abstract graphs. Using such techniques, however, the structural details of…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the…
Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…
The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of…
We use dual graphs and generating sequences of valuations to compute the Poincare series of non-divisorial valuations on function fields of dimension two. The Poincare series are shown to reflect data from the dual graphs and hence carry…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
In this article, we present a bifurcation analysis on the double-diffusive convection. Two pattern selections, rectangles and squares, are investigated. It is proved that there are two different types of attractor bifurcations depending on…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
This paper addresses the long-time behavior of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global…
Separatrices divide the phase space of some holomorphic dynamical systems into separate basins of attraction or 'stability regions' for distinct fixed points. 'Bundling' (high density) and mutual 'repulsion' of trajectories are often…
In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points with complex numbers via the assignment w = x+i y. In this…
We consider a deconvolution model for 3D periodic flows. We show the existence of a global attractor for the model.
A general recipe is developed for the study of rigid body dynamics in terms of Poincar\'e surfaces of section. A section condition is chosen which captures every trajectory on a given energy surface. The possible topological types of the…